Discriminant Analysis, a Powerful Classification Technique in Predictive Modeling

Discriminant analysis is one of the classical classification techniques used to discriminate a single categorical variable using multiple attributes. Discriminant analysis also assigns observations to one of the pre-defined groups based on the knowledge of the multi-attributes. When the distribution within each group is multivariate normal, a parametric method can be used to develop a discriminant function using a generalized squared distance measure. The classification criterion is derived based on either the individual within-group covariance matrices or the pooled covariance matrix that also takes into account the prior probabilities of the classes. Non-parametric discriminant methods are based on non-parametric groupspecific probability densities. Either a kernel or the k-nearest-neighbor method can be used to generate a non-parametric density estimate in each group and to produce a classification criterion. The performance of a discriminant criterion could be evaluated by estimating probabilities of mis-classification of new observations in the validation data. A user-friendly SAS application utilizing SAS macro to perform discriminant analysis is presented here. Chemical diabetes data containing multi-attributes is used to demonstrate the features of discriminant analysis in discriminating the three clinical types of diabetes.